Although most people use decimal arithmetic when performing manual calculations, computers typically only support binary arithmetic in hardware. This is primarily due to the fact that modern computers typically only represent two logic values: zero and one. While it is possible to use these two logic values to represent decimal numbers, doing so is wasteful in terms of storage space and often computationally less efficient. For example, in binary, four bits can represent sixteen values; while in binary coded decimal (BCD), four bits only represent ten values. Since most computer systems do not provide hardware support for decimal arithmetic, numbers are typically input in decimal, converted from decimal to binary, processed using binary arithmetic and then converted back to decimal for output.
In spite of the current dominance of hardware support for binary arithmetic, there are several motivations that encourage the provision of support for decimal arithmetic. First, applications that deal with financial and other real-world data often introduce errors since many common decimal numbers cannot be represented exactly in binary. For example, the decimal number “0.1” is a repeating fraction when represented in binary. Second, people typically think about computations in decimal, even when using computers that operate only on binary representations, and therefore may experience what is perceived as incorrect behavior when processing decimal values. Third, converting between binary and decimal floating-point numbers is computationally intensive. For example, conversion on modern processors may take thousands of processing cycles.
In an effort to alleviate some of the problems that occur when a computer only supports binary arithmetic in hardware, several software packages and programming language extensions for decimal arithmetic have been developed. Although some of these packages are successful in eliminating binary-to-decimal and decimal-to-binary conversion errors, the packages are often hundreds to thousands of times slower than binary operations implemented in hardware.